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Metamath Proof Explorer

Theorem ralrimivw

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 18-Jun-2014)

		Ref	Expression
	Hypothesis	ralrimivw.1	$⊢ φ \to ψ$
	Assertion	ralrimivw	$⊢ φ \to \forall x \in A ψ$

Step	Hyp	Ref	Expression
1		ralrimivw.1	$⊢ φ \to ψ$
2	1	a1d	$⊢ φ \to (x \in A \to ψ)$
3	2	ralrimiv	$⊢ φ \to \forall x \in A ψ$